This invention relates generally to amplifier linearization.
Radiofrequency power amplifiers are used in a wide variety of applications including, but not limited to, wireless communications and magnetic resonance imaging (MRI). The specifications for such diverse applications are different, but they have one common denominator: the need to maximize both the efficiency and linearity of increasingly powerful amplifiers. In the field of communications, linearity is demanded by the desire for high spectral efficiency, that is, the ability to transmit data at the highest possible rate for a given channel bandwidth. In the field of MRI, it is the increasingly popular use of arrays of coils to challenge the linearity of the power amplifiers driving these coils, because of the complex interactions between coils that change the load conditions (and induced output currents) significantly and unpredictably.
Many different linearization techniques have been proposed to deal with these challenges. Among them, Cartesian feedback has been proposed in both fields and has received a great deal of attention thanks to the great advantage that it does not require a detailed knowledge of the power amplifier behavior and is immune to its changes, such as those due to temperature and aging.
Classic Cartesian Feedback
Cartesian feedback is a method of linearizing highly-efficient nonlinear radio-frequency (RF) amplifiers. The basic principle of a Cartesian Feedback system is shown in FIG. 1. The quadrature baseband inputs, usually termed i and q components, form the reference signals for the loop. The forward path consists of the difference amplifiers, the synchronous up-mixer, the non-linear amplifier, and the output load (usually, but not always, an antenna). The difference amplifiers are characterized, to first order approximation, by the transfer function HC(ω) that describes the relationship between the complex output I+jQ and the complex input i+jq:
            H      C        ⁡          (      ω      )        =      K          1      +              j        ⁡                  (                      ω                          ω              O                                )                    
The feedback path consists of a coupler that sends a sample of the power amplifier output voltage (or current or linear combination thereof) to the synchronous down-mixer. The quadrature baseband components that result from this down-conversion are used as feedback signals and compared (subtracted) to the reference signals at the input of the difference amplifiers. The up-converted output of these amplifiers (the loop error signal) is thus the pre-distorted signal necessary to drive and linearize the power amplifier.
The last indispensable component of a Cartesian feedback system is the phase shifter. Synchronism between the up- and down-mixers is obtained by splitting a common RF carrier (the local oscillator, or LO, frequency), however the delays through the feedback and forward paths cause the reference and feedback signals to be phase misaligned, a situation that compromises the stability of the system. The phase shifter is thus necessary to compensate for the delays and maintain the correct relationship that guarantees the loop stability.
While there is a strong theoretical motivation to pursue Cartesian feedback, its penetration has been held back by the complexities associated with the actual implementation of the system. Issues such as the impact of phase misalignment on stability, phase and amplitude quadrature errors (particularly in the down-converter of the feedback path), and DC-offsets (particularly at the output of the multipliers and at the input of the difference amplifiers, also called error amplifiers) have been and still are the subject of many studies. The limit imposed by the accuracy of the down-conversion is fundamental to linearization strategies, as errors in the feedback path cannot be compensated by the loop operation and further complicate the analysis of the phase alignment control problem. DC-offsets also impact the quality of the output baseband spectrum.